PDE Boundary Control for Active Flutter Prevention Using Finite Dimensional Input-Output Maps

使用有限维输入输出图进行主动颤振预防的偏微分方程边界控制

• 批准号: EP/R032548/1
• 负责人: Aditya Paranjape
• 金额: $ 25.06万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FR032548%2F1
• 关键词: PDE; Boundary; Control; Active; Flutter

Flutter is a well-studied phenomenon in aircraft wings, and typically affects wings at high flight speeds. Traditionally, aircraft designers sought to avoid flutter altogether; if it was encountered at all during advanced design stages or flight testing, it was dealt with using design fixes and/or inefficient operational modifications. The importance of active flutter mitigation has increased as the wings have become lighter and consequently more flexible over the years. A recent example of active flutter mitigation, which is also commercially deployed, is the outboard aileron modal suppression (OAMS) system incorporated on the Boeing 747-8I. While the details of OAMS are unknown, the phrase "modal suppression" suggests that its design falls within the ambit of traditional wing control methods which use a finite dimensional approximation of the dynamics to design a stabilizing controller. Although this approach allows a designer to tap into the vast family of control techniques for systems described by ordinary differential equations (ODEs), it has three major drawbacks: the ODE approximations tend to have large orders, the states of the ODE are seldom physically meaningful, and the control design process is susceptible to spillover instabilities which can result from an improper modal approximation.Control techniques for systems described by partial differential equation (PDEs), and which avoid finite dimensional approximations, have been evolving steadily in the recent past and promise to do away with both aforementioned drawbacks. The prior work done by the PI led to two new adaptive control techniques that fall within this evolving family of techniques.One of the techniques developed by the PI uses finite dimensional input-output (FDIO) maps that arise naturally for specific input-output pairs for a given PDE. Using FDIO maps, it is possible to convert the control design problem exactly to one for ODEs. Although akin to the risky approach of designing a static output feedback controller in finite dimensional systems, the PI discovered that the structure of the PDE provides a means for expanding the stable envelope of the system even under static output feedback. The PI's work also provided a partial explanation for the underlying stabilization mechanism. The aim of the present project is to develop and demonstrate a low-order adaptive control design technique for flexible wings which exploits the underlying PDE structure of the dynamics effectively, together with a clever reformulation of the control problem. The controller would be based on the PI's prior work [1, 6]. We will provide a major extension of the technique to more realistic, 2-dof wing models and adaptive laws to help the controller deal with modeling and parametric uncertainties. This is key to ensuring practical applicability of the control technique, and requires non-trivial theoretical development as well. We will validate the control technique using wind tunnel testing. The outcome of this project would be a low-order adaptive controller accompanied by analytical performance and stability guarantees. Additionally, the control design would minimize the set of sensors required for the feedback laws, by avoiding ODE approximations as far as possible during the design process.Beneficiaries of this research include the academic community and the aircraft industry, notably those that are involved in developing and deploying aeroelastic solutions. The broader impact of the proposed research has been described elsewhere in the proposal.

Flutter是飞机​​翅膀中的一种认真的现象，通常会以高飞行速度影响翅膀。传统上，飞机设计师试图避免完全颤动。如果在高级设计阶段或飞行测试中完全遇到了它，则使用设计修复程序和/或效率低下的操作修改处理。随着翅膀在多年来变得更轻，更加灵活，主动颤动缓解的重要性已经增加。在波音747-8i上纳入的舷外aileron模态抑制（OAMS）系统，这也是商业部署的活动颤动缓解措施的最新示例。虽然OAM的细节尚不清楚，但短语“模态抑制”表明其设计属于传统的机翼控制方法的范围，该方法使用动力学的有限维度近似来设计稳定控制器。尽管这种方法使设计师可以利用普通微分方程（ODE）描述的系统的庞大控制技术，但它具有三个主要缺点：颂歌近似倾向于具有较大的阶数，该状态很少有意义，并且在物理上有意义，并且通过溢出的质量分离效果，这些过程可能会导致不利的模块化技术的差异。 （PDE）并避免有限的维近似值，在最近的过去一直在稳步发展，并有望消除上述两个缺点。 PI所做的先前的工作导致了两种新的自适应控制技术属于这种不断发展的技术家族。PI开发的技术使用有限的尺寸输入输出（FDIO）映射（FDIO）图，这些图自然而然地用于特定的输入输出对，用于给定的PDE。使用FDIO地图，可以将控制设计问题精确地转换为ODE的一个。尽管类似于在有限尺寸系统中设计静态输出反馈控制器的危险方法，但PI发现PDE的结构即使在静态输出反馈下，PDE的结构也提供了一种扩展系统稳定信封的方法。 PI的工作还为基础稳定机制提供了部分解释。本项目的目的是为灵活的机翼开发和展示一种低阶自适应控制设计技术，该技术可以有效利用动力学的基础PDE结构，并巧妙地重新重新进行控制问题。控制器将基于PI的先前工作[1，6]。我们将向更现实的二-DOF机翼模型和自适应定律提供该技术的主要扩展，以帮助控制器处理建模和参数不确定性。这是确保控制技术的实际适用性的关键，并且还需要非平凡的理论发展。我们将使用风洞测试验证控制技术。该项目的结果将是一个低阶自适应控制器，并伴有分析性能和稳定性保证。此外，控制设计将通过在设计过程中尽可能避免使用ODE近似值来最大程度地降低反馈法律所需的传感器集。这项研究的知识包括学术界和飞机行业，尤其​​是那些参与开发和部署Aero弹性解决方案的行业。该提案的其他地方描述了拟议研究的更广泛影响。